Abstract

A simple rate equation model is used to determine the macroscopic upconversion parameter of a heavily erbium-doped oxyfluoride transparent glass ceramic. The fraction of initially excited ions in the metastable state among erbium ions partitioned in the nanocrystallite phase is found and the decay of the S324 level is used to determine the upconversion parameter. The macroscopic energy-transfer upconversion parameter is found to be approximately 4×1018cm3s1, in good agreement with other erbium-doped fluoride materials.

© 2006 Optical Society of America

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  1. Y. Wang and J. Ohwaki, "New transparent vitroceramics codoped with Er3+ and Yb3+ for efficient frequency upconversion," Appl. Phys. Lett. 63, 3268-3270 (1993).
    [CrossRef]
  2. M. Dejneka, "Transparent oxyfluoride glass ceramics," MRS Bull. 23, 57-62 (1998).
  3. G. C. Jones and S. N. Houde-Walter, "Upconversion mechanisms in an erbium-doped transparent glass ceramic," J. Opt. Soc. Am. B 22, 825-830 (2005).
    [CrossRef]
  4. G. C. Jones and S. N. Houde-Walter, "Erbium partitioning in a heavily doped transparent glass ceramic," Opt. Lett. 30, 2122-2124 (2005).
    [CrossRef] [PubMed]
  5. W. Lüthy and H. P. Weber, "The 3μm erbium laser," Infrared Phys. 32, 283-290 (1991).
    [CrossRef]
  6. B. R. Judd, "Optical absorption intensities of rare-earth ions," Phys. Rev. 127, 750-761 (1962).
    [CrossRef]
  7. G. S. Ofelt, "Intensities of crystal spectra of rare earth ions," J. Chem. Phys. 37, 511-520 (1962).
    [CrossRef]
  8. W. T. Carnall, H. Crosswhite, and H. M. Crosswhite, "Energy level structure and transition probabilities of the trivalent lanthanides in LaF3," Report ANL-78-95 (Argonne National Laboratory, 1979).
  9. M. J. Weber, "Probabilities for radiative and nonradiative decay of Er3+ in LaF3," Phys. Rev. 157, 262-272 (1967).
    [CrossRef]
  10. M. P. Hehlen, N. J. Cockroft, T. R. Gosnell, and A. J. Bruce, "Spectroscopic properties of Er3+-and Yb3+-doped soda-lime and aluminosilicate glasses," Phys. Rev. B 56, 9302-9318 (1997).
    [CrossRef]
  11. L. A. Riseberg and M. J. Weber, "Relaxation phenomena in rare-earth luminescence," in Progress in Optics (North-Holland, 1976), Vol. 14, pp. 91-159.
  12. P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, "Energy transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses," Phys. Rev. B 62, 856-864 (2000).
    [CrossRef]
  13. T. Jensen, Ph.D. dissertation (Institute of Laser-Physics, University of Hamburg, 1996).
  14. Because the detector imperfectly compensates for dc offsets, the baseline level would shift toward the rms voltage of the input signal, so the baseline will begin to rise at the onset of the fluorescence. The negative portion of the output signal rises because for a short period of time the input signal level had dipped below that of the shifting baseline. The data were fitted over a long time period to minimize this effect.
  15. R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, 1986).
  16. J. M. F. van Dijk and M. F. H. Schuurmans, "On the nonradiative and radiative decay rates and a modified exponential energy gap law for 4f-4f transitions in rare-earth ions," J. Chem. Phys. 78, 5317-5323 (1983).
    [CrossRef]
  17. E. I. Kamitsos, J. A. Kapoutsis, H. Jain, and C. H. Hsieh, "Vibrational study of the role of the trivalent ions in sodium trisilicate glass," J. Non-Cryst. Solids 171, 31-45 (1994).
    [CrossRef]
  18. D. E. McCumber, "Theory of phonon-terminated optical masers," Phys. Rev. 134, A299-A306 (1964).
    [CrossRef]
  19. W. J. Miniscalco and R. S. Quimby, "General procedure for the analysis of Er3+ cross sections," Opt. Lett. 16, 258-260 (1991).
    [CrossRef] [PubMed]
  20. P. A. Tick, N. F. Borrelli, and I. M. Reaney, "The relationship between structure and transparency in glass-ceramic materials," Opt. Mater. 15, 81-91 (2000).
    [CrossRef]
  21. V. K. Bogdanov, D. J. Booth, and W. E. K. Gibbs, "Energy transfer processes and the green fluorescence in heavily doped Er3+: fluoride glasses," J. Non-Cryst. Solids 321, 20-28 (2003).
    [CrossRef]
  22. G. F. Simmons, Differential Equations with Applications and Historical Notes, 2nd ed. (McGraw-Hill, 1991).
  23. V. K. Bogdanov, D. J. Booth, W. E. K. Gibbs, J. S. Javorniczky, P. J. Newman, and D. R. MacFarlane, "Population dynamics in Er3+-doped fluoride glasses," Phys. Rev. B 63, 205107-205121 (2001).
    [CrossRef]
  24. F. Enrichi and E. Borsella, "A simple approach for upconversion determination using low excitation power: the photoluminescence analysis of and Er-doped aluminosilicate glass," Mater. Sci. Eng. B 105, 20-24 (2003).
    [CrossRef]

2005 (2)

2003 (2)

F. Enrichi and E. Borsella, "A simple approach for upconversion determination using low excitation power: the photoluminescence analysis of and Er-doped aluminosilicate glass," Mater. Sci. Eng. B 105, 20-24 (2003).
[CrossRef]

V. K. Bogdanov, D. J. Booth, and W. E. K. Gibbs, "Energy transfer processes and the green fluorescence in heavily doped Er3+: fluoride glasses," J. Non-Cryst. Solids 321, 20-28 (2003).
[CrossRef]

2001 (1)

V. K. Bogdanov, D. J. Booth, W. E. K. Gibbs, J. S. Javorniczky, P. J. Newman, and D. R. MacFarlane, "Population dynamics in Er3+-doped fluoride glasses," Phys. Rev. B 63, 205107-205121 (2001).
[CrossRef]

2000 (2)

P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, "Energy transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses," Phys. Rev. B 62, 856-864 (2000).
[CrossRef]

P. A. Tick, N. F. Borrelli, and I. M. Reaney, "The relationship between structure and transparency in glass-ceramic materials," Opt. Mater. 15, 81-91 (2000).
[CrossRef]

1998 (1)

M. Dejneka, "Transparent oxyfluoride glass ceramics," MRS Bull. 23, 57-62 (1998).

1997 (1)

M. P. Hehlen, N. J. Cockroft, T. R. Gosnell, and A. J. Bruce, "Spectroscopic properties of Er3+-and Yb3+-doped soda-lime and aluminosilicate glasses," Phys. Rev. B 56, 9302-9318 (1997).
[CrossRef]

1994 (1)

E. I. Kamitsos, J. A. Kapoutsis, H. Jain, and C. H. Hsieh, "Vibrational study of the role of the trivalent ions in sodium trisilicate glass," J. Non-Cryst. Solids 171, 31-45 (1994).
[CrossRef]

1993 (1)

Y. Wang and J. Ohwaki, "New transparent vitroceramics codoped with Er3+ and Yb3+ for efficient frequency upconversion," Appl. Phys. Lett. 63, 3268-3270 (1993).
[CrossRef]

1991 (2)

1983 (1)

J. M. F. van Dijk and M. F. H. Schuurmans, "On the nonradiative and radiative decay rates and a modified exponential energy gap law for 4f-4f transitions in rare-earth ions," J. Chem. Phys. 78, 5317-5323 (1983).
[CrossRef]

1967 (1)

M. J. Weber, "Probabilities for radiative and nonradiative decay of Er3+ in LaF3," Phys. Rev. 157, 262-272 (1967).
[CrossRef]

1964 (1)

D. E. McCumber, "Theory of phonon-terminated optical masers," Phys. Rev. 134, A299-A306 (1964).
[CrossRef]

1962 (2)

B. R. Judd, "Optical absorption intensities of rare-earth ions," Phys. Rev. 127, 750-761 (1962).
[CrossRef]

G. S. Ofelt, "Intensities of crystal spectra of rare earth ions," J. Chem. Phys. 37, 511-520 (1962).
[CrossRef]

Bogdanov, V. K.

V. K. Bogdanov, D. J. Booth, and W. E. K. Gibbs, "Energy transfer processes and the green fluorescence in heavily doped Er3+: fluoride glasses," J. Non-Cryst. Solids 321, 20-28 (2003).
[CrossRef]

V. K. Bogdanov, D. J. Booth, W. E. K. Gibbs, J. S. Javorniczky, P. J. Newman, and D. R. MacFarlane, "Population dynamics in Er3+-doped fluoride glasses," Phys. Rev. B 63, 205107-205121 (2001).
[CrossRef]

Booth, D. J.

V. K. Bogdanov, D. J. Booth, and W. E. K. Gibbs, "Energy transfer processes and the green fluorescence in heavily doped Er3+: fluoride glasses," J. Non-Cryst. Solids 321, 20-28 (2003).
[CrossRef]

V. K. Bogdanov, D. J. Booth, W. E. K. Gibbs, J. S. Javorniczky, P. J. Newman, and D. R. MacFarlane, "Population dynamics in Er3+-doped fluoride glasses," Phys. Rev. B 63, 205107-205121 (2001).
[CrossRef]

Borrelli, N. F.

P. A. Tick, N. F. Borrelli, and I. M. Reaney, "The relationship between structure and transparency in glass-ceramic materials," Opt. Mater. 15, 81-91 (2000).
[CrossRef]

Borsella, E.

F. Enrichi and E. Borsella, "A simple approach for upconversion determination using low excitation power: the photoluminescence analysis of and Er-doped aluminosilicate glass," Mater. Sci. Eng. B 105, 20-24 (2003).
[CrossRef]

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, 1986).

Bruce, A. J.

M. P. Hehlen, N. J. Cockroft, T. R. Gosnell, and A. J. Bruce, "Spectroscopic properties of Er3+-and Yb3+-doped soda-lime and aluminosilicate glasses," Phys. Rev. B 56, 9302-9318 (1997).
[CrossRef]

Carnall, W. T.

W. T. Carnall, H. Crosswhite, and H. M. Crosswhite, "Energy level structure and transition probabilities of the trivalent lanthanides in LaF3," Report ANL-78-95 (Argonne National Laboratory, 1979).

Cockroft, N. J.

M. P. Hehlen, N. J. Cockroft, T. R. Gosnell, and A. J. Bruce, "Spectroscopic properties of Er3+-and Yb3+-doped soda-lime and aluminosilicate glasses," Phys. Rev. B 56, 9302-9318 (1997).
[CrossRef]

Crosswhite, H.

W. T. Carnall, H. Crosswhite, and H. M. Crosswhite, "Energy level structure and transition probabilities of the trivalent lanthanides in LaF3," Report ANL-78-95 (Argonne National Laboratory, 1979).

Crosswhite, H. M.

W. T. Carnall, H. Crosswhite, and H. M. Crosswhite, "Energy level structure and transition probabilities of the trivalent lanthanides in LaF3," Report ANL-78-95 (Argonne National Laboratory, 1979).

Dejneka, M.

M. Dejneka, "Transparent oxyfluoride glass ceramics," MRS Bull. 23, 57-62 (1998).

Enrichi, F.

F. Enrichi and E. Borsella, "A simple approach for upconversion determination using low excitation power: the photoluminescence analysis of and Er-doped aluminosilicate glass," Mater. Sci. Eng. B 105, 20-24 (2003).
[CrossRef]

Gibbs, W. E. K.

V. K. Bogdanov, D. J. Booth, and W. E. K. Gibbs, "Energy transfer processes and the green fluorescence in heavily doped Er3+: fluoride glasses," J. Non-Cryst. Solids 321, 20-28 (2003).
[CrossRef]

V. K. Bogdanov, D. J. Booth, W. E. K. Gibbs, J. S. Javorniczky, P. J. Newman, and D. R. MacFarlane, "Population dynamics in Er3+-doped fluoride glasses," Phys. Rev. B 63, 205107-205121 (2001).
[CrossRef]

Golding, P. S.

P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, "Energy transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses," Phys. Rev. B 62, 856-864 (2000).
[CrossRef]

Gosnell, T. R.

M. P. Hehlen, N. J. Cockroft, T. R. Gosnell, and A. J. Bruce, "Spectroscopic properties of Er3+-and Yb3+-doped soda-lime and aluminosilicate glasses," Phys. Rev. B 56, 9302-9318 (1997).
[CrossRef]

Hehlen, M. P.

M. P. Hehlen, N. J. Cockroft, T. R. Gosnell, and A. J. Bruce, "Spectroscopic properties of Er3+-and Yb3+-doped soda-lime and aluminosilicate glasses," Phys. Rev. B 56, 9302-9318 (1997).
[CrossRef]

Houde-Walter, S. N.

Hsieh, C. H.

E. I. Kamitsos, J. A. Kapoutsis, H. Jain, and C. H. Hsieh, "Vibrational study of the role of the trivalent ions in sodium trisilicate glass," J. Non-Cryst. Solids 171, 31-45 (1994).
[CrossRef]

Jackson, S. D.

P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, "Energy transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses," Phys. Rev. B 62, 856-864 (2000).
[CrossRef]

Jain, H.

E. I. Kamitsos, J. A. Kapoutsis, H. Jain, and C. H. Hsieh, "Vibrational study of the role of the trivalent ions in sodium trisilicate glass," J. Non-Cryst. Solids 171, 31-45 (1994).
[CrossRef]

Javorniczky, J. S.

V. K. Bogdanov, D. J. Booth, W. E. K. Gibbs, J. S. Javorniczky, P. J. Newman, and D. R. MacFarlane, "Population dynamics in Er3+-doped fluoride glasses," Phys. Rev. B 63, 205107-205121 (2001).
[CrossRef]

Jensen, T.

T. Jensen, Ph.D. dissertation (Institute of Laser-Physics, University of Hamburg, 1996).

Jones, G. C.

Judd, B. R.

B. R. Judd, "Optical absorption intensities of rare-earth ions," Phys. Rev. 127, 750-761 (1962).
[CrossRef]

Kamitsos, E. I.

E. I. Kamitsos, J. A. Kapoutsis, H. Jain, and C. H. Hsieh, "Vibrational study of the role of the trivalent ions in sodium trisilicate glass," J. Non-Cryst. Solids 171, 31-45 (1994).
[CrossRef]

Kapoutsis, J. A.

E. I. Kamitsos, J. A. Kapoutsis, H. Jain, and C. H. Hsieh, "Vibrational study of the role of the trivalent ions in sodium trisilicate glass," J. Non-Cryst. Solids 171, 31-45 (1994).
[CrossRef]

King, T. A.

P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, "Energy transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses," Phys. Rev. B 62, 856-864 (2000).
[CrossRef]

Lüthy, W.

W. Lüthy and H. P. Weber, "The 3μm erbium laser," Infrared Phys. 32, 283-290 (1991).
[CrossRef]

MacFarlane, D. R.

V. K. Bogdanov, D. J. Booth, W. E. K. Gibbs, J. S. Javorniczky, P. J. Newman, and D. R. MacFarlane, "Population dynamics in Er3+-doped fluoride glasses," Phys. Rev. B 63, 205107-205121 (2001).
[CrossRef]

McCumber, D. E.

D. E. McCumber, "Theory of phonon-terminated optical masers," Phys. Rev. 134, A299-A306 (1964).
[CrossRef]

Miniscalco, W. J.

Newman, P. J.

V. K. Bogdanov, D. J. Booth, W. E. K. Gibbs, J. S. Javorniczky, P. J. Newman, and D. R. MacFarlane, "Population dynamics in Er3+-doped fluoride glasses," Phys. Rev. B 63, 205107-205121 (2001).
[CrossRef]

Ofelt, G. S.

G. S. Ofelt, "Intensities of crystal spectra of rare earth ions," J. Chem. Phys. 37, 511-520 (1962).
[CrossRef]

Ohwaki, J.

Y. Wang and J. Ohwaki, "New transparent vitroceramics codoped with Er3+ and Yb3+ for efficient frequency upconversion," Appl. Phys. Lett. 63, 3268-3270 (1993).
[CrossRef]

Pollnau, M.

P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, "Energy transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses," Phys. Rev. B 62, 856-864 (2000).
[CrossRef]

Quimby, R. S.

Reaney, I. M.

P. A. Tick, N. F. Borrelli, and I. M. Reaney, "The relationship between structure and transparency in glass-ceramic materials," Opt. Mater. 15, 81-91 (2000).
[CrossRef]

Riseberg, L. A.

L. A. Riseberg and M. J. Weber, "Relaxation phenomena in rare-earth luminescence," in Progress in Optics (North-Holland, 1976), Vol. 14, pp. 91-159.

Schuurmans, M. F. H.

J. M. F. van Dijk and M. F. H. Schuurmans, "On the nonradiative and radiative decay rates and a modified exponential energy gap law for 4f-4f transitions in rare-earth ions," J. Chem. Phys. 78, 5317-5323 (1983).
[CrossRef]

Simmons, G. F.

G. F. Simmons, Differential Equations with Applications and Historical Notes, 2nd ed. (McGraw-Hill, 1991).

Tick, P. A.

P. A. Tick, N. F. Borrelli, and I. M. Reaney, "The relationship between structure and transparency in glass-ceramic materials," Opt. Mater. 15, 81-91 (2000).
[CrossRef]

van Dijk, J. M. F.

J. M. F. van Dijk and M. F. H. Schuurmans, "On the nonradiative and radiative decay rates and a modified exponential energy gap law for 4f-4f transitions in rare-earth ions," J. Chem. Phys. 78, 5317-5323 (1983).
[CrossRef]

Wang, Y.

Y. Wang and J. Ohwaki, "New transparent vitroceramics codoped with Er3+ and Yb3+ for efficient frequency upconversion," Appl. Phys. Lett. 63, 3268-3270 (1993).
[CrossRef]

Weber, H. P.

W. Lüthy and H. P. Weber, "The 3μm erbium laser," Infrared Phys. 32, 283-290 (1991).
[CrossRef]

Weber, M. J.

M. J. Weber, "Probabilities for radiative and nonradiative decay of Er3+ in LaF3," Phys. Rev. 157, 262-272 (1967).
[CrossRef]

L. A. Riseberg and M. J. Weber, "Relaxation phenomena in rare-earth luminescence," in Progress in Optics (North-Holland, 1976), Vol. 14, pp. 91-159.

Appl. Phys. Lett. (1)

Y. Wang and J. Ohwaki, "New transparent vitroceramics codoped with Er3+ and Yb3+ for efficient frequency upconversion," Appl. Phys. Lett. 63, 3268-3270 (1993).
[CrossRef]

Infrared Phys. (1)

W. Lüthy and H. P. Weber, "The 3μm erbium laser," Infrared Phys. 32, 283-290 (1991).
[CrossRef]

J. Chem. Phys. (2)

G. S. Ofelt, "Intensities of crystal spectra of rare earth ions," J. Chem. Phys. 37, 511-520 (1962).
[CrossRef]

J. M. F. van Dijk and M. F. H. Schuurmans, "On the nonradiative and radiative decay rates and a modified exponential energy gap law for 4f-4f transitions in rare-earth ions," J. Chem. Phys. 78, 5317-5323 (1983).
[CrossRef]

J. Non-Cryst. Solids (2)

E. I. Kamitsos, J. A. Kapoutsis, H. Jain, and C. H. Hsieh, "Vibrational study of the role of the trivalent ions in sodium trisilicate glass," J. Non-Cryst. Solids 171, 31-45 (1994).
[CrossRef]

V. K. Bogdanov, D. J. Booth, and W. E. K. Gibbs, "Energy transfer processes and the green fluorescence in heavily doped Er3+: fluoride glasses," J. Non-Cryst. Solids 321, 20-28 (2003).
[CrossRef]

J. Opt. Soc. Am. B (1)

Mater. Sci. Eng. B (1)

F. Enrichi and E. Borsella, "A simple approach for upconversion determination using low excitation power: the photoluminescence analysis of and Er-doped aluminosilicate glass," Mater. Sci. Eng. B 105, 20-24 (2003).
[CrossRef]

MRS Bull. (1)

M. Dejneka, "Transparent oxyfluoride glass ceramics," MRS Bull. 23, 57-62 (1998).

Opt. Lett. (2)

Opt. Mater. (1)

P. A. Tick, N. F. Borrelli, and I. M. Reaney, "The relationship between structure and transparency in glass-ceramic materials," Opt. Mater. 15, 81-91 (2000).
[CrossRef]

Phys. Rev. (3)

D. E. McCumber, "Theory of phonon-terminated optical masers," Phys. Rev. 134, A299-A306 (1964).
[CrossRef]

M. J. Weber, "Probabilities for radiative and nonradiative decay of Er3+ in LaF3," Phys. Rev. 157, 262-272 (1967).
[CrossRef]

B. R. Judd, "Optical absorption intensities of rare-earth ions," Phys. Rev. 127, 750-761 (1962).
[CrossRef]

Phys. Rev. B (3)

P. S. Golding, S. D. Jackson, T. A. King, and M. Pollnau, "Energy transfer processes in Er3+-doped and Er3+, Pr3+-codoped ZBLAN glasses," Phys. Rev. B 62, 856-864 (2000).
[CrossRef]

M. P. Hehlen, N. J. Cockroft, T. R. Gosnell, and A. J. Bruce, "Spectroscopic properties of Er3+-and Yb3+-doped soda-lime and aluminosilicate glasses," Phys. Rev. B 56, 9302-9318 (1997).
[CrossRef]

V. K. Bogdanov, D. J. Booth, W. E. K. Gibbs, J. S. Javorniczky, P. J. Newman, and D. R. MacFarlane, "Population dynamics in Er3+-doped fluoride glasses," Phys. Rev. B 63, 205107-205121 (2001).
[CrossRef]

Other (6)

L. A. Riseberg and M. J. Weber, "Relaxation phenomena in rare-earth luminescence," in Progress in Optics (North-Holland, 1976), Vol. 14, pp. 91-159.

G. F. Simmons, Differential Equations with Applications and Historical Notes, 2nd ed. (McGraw-Hill, 1991).

T. Jensen, Ph.D. dissertation (Institute of Laser-Physics, University of Hamburg, 1996).

Because the detector imperfectly compensates for dc offsets, the baseline level would shift toward the rms voltage of the input signal, so the baseline will begin to rise at the onset of the fluorescence. The negative portion of the output signal rises because for a short period of time the input signal level had dipped below that of the shifting baseline. The data were fitted over a long time period to minimize this effect.

R. N. Bracewell, The Fourier Transform and Its Applications, 2nd ed. (McGraw-Hill, 1986).

W. T. Carnall, H. Crosswhite, and H. M. Crosswhite, "Energy level structure and transition probabilities of the trivalent lanthanides in LaF3," Report ANL-78-95 (Argonne National Laboratory, 1979).

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Figures (6)

Fig. 1
Fig. 1

Energy-level diagram of Er 3 + : LaF 3 , with approximations made for low-temperature pulsed infrared pumping. The broken line indicates an absorption by F 7 2 4 and subsequent fast decay to S 3 2 4 .

Fig. 2
Fig. 2

Fluorescence decay at 2.975.8 nm from the I 11 2 4 level in the Er 3 + -doped transparent glass ceramic at 10 K .

Fig. 3
Fig. 3

Fluorescence intensity at 10 K of the I 11 2 4 level. Gated integrator gate delay times are indicated.

Fig. 4
Fig. 4

Absorption cross sections for the I 15 2 4 I 11 2 4 absorption transition in Er 3 + ions in the aluminosilicate glass phase (dashed curve) and the LaF 3 nanocrystal phase (solid curve) of the transparent glass ceramic measured at 10 K .

Fig. 5
Fig. 5

Gray data points are the measured 539 nm fluorescence decays produced under upconversion pumping by the wavelength indicated in the figure, at 8 mW average power and at a temperature of 10 K . The black curves are fits to the data using Eqs. (3). Values of C up , n 30 , and n 20 for each excitation wavelength are given in Table 2.

Fig. 6
Fig. 6

Fluorescence decays at 10 K from the I 11 2 4 state produced under excitation to the I 9 2 4 level (black curve) and under upconversion pumping conditions (gray curve).

Tables (2)

Tables Icon

Table 1 Relevant Transition Rates and Lifetimes for Er 3 + : LaF 3

Tables Icon

Table 2 Pump Wavelength, Absorption Cross Sections, and n 20 Used in the Fits shown in Fig. 5 a

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

W NR = C e α ( Δ E 2 ω i ) ( 1 e ω i kT ) Δ E ω i ,
N ̇ 3 = N 3 τ 3 + C up N 2 2 ,
N ̇ 2 = N 2 τ 2 2 C up N 2 2 ,
n ̇ 3 = n 3 τ 3 + C up N nc n 2 2 ,
n ̇ 2 = n 2 τ 2 2 C up N nc n 2 2 ,
( G xtal e t τ xtal + G glass e t τ glass ) D e t τ set = G xtal D e t τ xtal 1 τ det 1 τ xtal + G glass D e t τ glass 1 τ det 1 τ glass ( G xtal D 1 τ det 1 τ xtal + G glass D 1 τ det 1 τ glass ) e t τ set ,
I ( l ) = I 0 exp ( α glass + α nc ) l ,
I abs , nc ( l ) = Δ l α nc I ( l ) .
I total , nc = 0 L I abs , nc ( l ) Δ l d l
= 0 L V nc σ abs , nc N Er , nc I ( l ) d l = I 0 ( V nc σ abs , nc N Er , nc V nc σ abs , nc N Er , nc + V glass σ abs , glass N Er , glass ) [ 1 e ( V nc σ nc N Er , nc + V glass σ abs , glass N Er , glass ) L ] .
n 20 = W 0 R A L h ν p ( σ abs , nc V nc σ abs , nc N Er , nc + V glass σ abs , glass N Er , glass ) [ 1 e ( α nc + α glass ) L ] .
β rad τ = 8 π n 2 c 2 0 ν 2 σ e ( ν ) d ν ,
g 1 ν 2 σ a ( ν ) d ν = g 2 ν 2 σ e ( ν ) d ν ,
n 2 ( t ) = n 20 e t τ 2 1 + 2 C up N Er , nc n 20 τ 2 [ 1 e t τ 2 ] .

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